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A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state
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Ortner, Christoph and Wollner, W. (2011) A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state. Numerische Mathematik, Volume 118 (Number 3). pp. 587-600. doi:10.1007/s00211-011-0360-9 ISSN 0029-599X.
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Official URL: http://dx.doi.org/10.1007/s00211-011-0360-9
Abstract
We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W 1,ā-error of the finite element projection, without using adjoint information. If the control space is discretized directly, we first prove a regularity result for the optimal control to control the approximation error, based on which we then obtain analogous convergence rates.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Finite element method, Differential equations, Partial | ||||
Journal or Publication Title: | Numerische Mathematik | ||||
Publisher: | Springer | ||||
ISSN: | 0029-599X | ||||
Official Date: | July 2011 | ||||
Dates: |
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Volume: | Volume 118 | ||||
Number: | Number 3 | ||||
Page Range: | pp. 587-600 | ||||
DOI: | 10.1007/s00211-011-0360-9 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 20 December 2015 | ||||
Date of first compliant Open Access: | 20 December 2015 | ||||
Funder: | Deutsche Forschungsgemeinschaft (DFG), Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | 1253 (DFG) |
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